## PDM-iRZ-QPSK vs. PS-QPSK at 100 Gbit/s over dispersion-managed links |

Optics Express, Vol. 20, Issue 7, pp. 7895-7900 (2012)

http://dx.doi.org/10.1364/OE.20.007895

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### Abstract

We compare by simulation the performance of 100Gbit/s PDM-iRZ-QPSK and PS-QPSK transmission both in homogeneous and hybrid QPSK/OOK DM links. We detail the reasons of the overall performance investigating each nonlinear effect (SPM, XPM and XPolM) individually. Moreover, we compare the accuracy of the noise loading method with the more realistic use of noisy in-line amplifiers. Results shows that i) PDM-iRZ-QPSK and PS-QPSK have same reach in both homogeneous and hybrid setups, ii) correct simulations must include distributed ASE.

© 2012 OSA

## 1. Introduction

*homogeneous*channels, and with a

*hybrid*scheme with a central QPSK channel surrounded by 10Gb/s on-off keying (OOK) channels. We will use the nonlinearity-decoupling method [8] to understand the role of the main nonlinearities, namely, self-phase modulation (SPM), cross-phase modulation (XPM) and XPolM. We also investigate the accuracy of the fast noise-loading simulation technique against the computationally-heavy true case of distributed noise generation at in-line amplifiers.

## 2. Simulations setup

*N*standard single mode fiber (SSMF) spans of 100 km each, with a typical in-line residual dispersion

*D*= 30 ps/nm/span. Before transmission we inserted a pre-compensating fiber of −369 − (

_{in}*N*− 1)

*D*/2 ps/nm [8]. The value of

_{in}*N*was varied in the range 20 to 60. At the end of the link, an ideal post-compensating fiber set the total cumulated dispersion to zero. Fiber propagation was implemented with the separate-field solution [9

9. P. Serena, M. Bertolini, and A. Vannucci, “Optilux toolbox,” (2009). [online] www.optilux.sourceforge.net.

10. P. Serena, N. Rossi, O. Bertran-Pardo, J. Renaudier, A. Vannucci, and A. Bononi, “Intra- versus Inter-channel PMD in Linearly Compensated Coherent PDM-PSK Nonlinear Transmissions,” J. Lightwave Technol. **29**(11), 1691–1700 (2011). [CrossRef]

^{nd}order super-Gaussian filter of bandwidth 0.4 nm. Before detection we used an optical filter of bandwidth 1.8

*R*that extracted the central WDM channel,

*R*being the symbol rate.

*R*GHz, sampling at 2 samples per symbols, polarization recovery through a 7-taps CMA [11

11. P. Johannisson, M. Sjödin, M. Karlsson, H. Wymeersch, E. Agrell, and P. A. Andrekson, “Modified constant modulus algorithm for polarization-switched QPSK,” Opt. Express **19**(8), 7734–7741 (2011). [CrossRef] [PubMed]

12. A. J. Viterbi and A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory **29**(4), 543–551 (1983). [CrossRef]

9. P. Serena, M. Bertolini, and A. Vannucci, “Optilux toolbox,” (2009). [online] www.optilux.sourceforge.net.

## 3. Results

2. E. Agrell and M. Karlsson, “Power-efficient modulation formats in coherent transmission systems,” J. Lightwave Technol. **27**(22), 5115–5126 (2009). [CrossRef]

## 4. Conclusions

## Appendix

*h*(

*t*) models the analog digital converters (ADC) response.

*x*(

*t*) and

*y*(

*t*) are the two PDM-QPSK tributaries, while the Dirac delta

*δ*(

*t*±

*τ*) indicates the impulse response of a delay line of

*τ*seconds. This scheme works both with/without pulse interleaving: in the first case

*τ*= 0, while for iRZ

*τ*is half a symbol time:

*τ*|

*=*

_{iRZ}*T*/2. After sampling at

*t*=

*t*, for iRZ shaping we have the following signals:

_{k}*x*(

*t*)

*,y*(

*t*)]. We expect the crosstalk to spread the SOP over the Poincaré sphere, thus compromising the demultiplexing.

*τ*= 0, hence we have the following: For practical not too narrow LPF, the net result of filtering is essentially an energy loss around sampling times, such that

*x*(

*t*) ⊗

*h*(

*t*)|

_{tk}≃

*x*(

*t*)

_{k}*c*and

*y*(

*t*) ⊗

*h*(

*t*)|

_{tk}≃

*y*(

*t*)

_{k}*c*, being

*c*a constant. See Fig. 6 for example. But a constant like

*c*impacts equally signal and noise, thus leaving a “clean” SOP over the Poincaré sphere as for a generic rotation. Figure 7 (left) confirms the claim showing that there is no SOP spreading, i.e., no polarization crosstalk.

## References and links

1. | M. Karlsson and E. Agrell, “Which is the most power-efficient modulation format in optical links?” Opt. Express |

2. | E. Agrell and M. Karlsson, “Power-efficient modulation formats in coherent transmission systems,” J. Lightwave Technol. |

3. | P. Poggiolini, G. Bosco, A. Carena, V. Curri, and F. Forghieri, “Performance evaluation of coherent WDM PS-QPSK (HEXA) accounting for non-linear fiber propagation effects,” Opt. Express |

4. | P. Serena, A. Vannucci, and A. Bononi, “The performance of polarization switched-QPSK (PS-QPSK) in dispersion managed WDM transmissions,” in Proc. ECOC 2010, Torino, Italy, (2010). Paper Th.10.E.2. |

5. | D. S. Millar, D. Lavery, S. Makovejs, C. Behrens, B. C. Thomsen, P. Bayvel, and S. J. Savory, “Generation and long-haul transmission of polarization-switched QPSK at 42.9 Gb/s,” Opt. Express |

6. | C. Xie, “Interchannel nonlinearities in coherent polarization-division-multiplexed quadrature-phase-shift- keying systems,” IEEE Photon. Technol. Lett. |

7. | O. Bertran-Pardo, J. Renaudier, G. Charlet, P. Tran, H. Mardoyan, M. Salsi, M. Bertolini, and S. Bigo, “Insertion of 100Gb/s coherent PDM-QPSK channels over legacy optical networks relying on low chromatic dispersion fibres,” in Proc. IEEE Globecom , (2009). |

8. | A. Bononi, N. Rossi, and P. Serena, “Transmission limitations due to fiber nonlinearity,” in Proc. OFC-NFOEC 2011, Los Angeles, CA, (2011). Paper OWO7. |

9. | P. Serena, M. Bertolini, and A. Vannucci, “Optilux toolbox,” (2009). [online] www.optilux.sourceforge.net. |

10. | P. Serena, N. Rossi, O. Bertran-Pardo, J. Renaudier, A. Vannucci, and A. Bononi, “Intra- versus Inter-channel PMD in Linearly Compensated Coherent PDM-PSK Nonlinear Transmissions,” J. Lightwave Technol. |

11. | P. Johannisson, M. Sjödin, M. Karlsson, H. Wymeersch, E. Agrell, and P. A. Andrekson, “Modified constant modulus algorithm for polarization-switched QPSK,” Opt. Express |

12. | A. J. Viterbi and A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory |

**OCIS Codes**

(060.1660) Fiber optics and optical communications : Coherent communications

(060.2330) Fiber optics and optical communications : Fiber optics communications

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: September 14, 2011

Revised Manuscript: December 16, 2011

Manuscript Accepted: December 17, 2011

Published: March 21, 2012

**Citation**

P. Serena, N. Rossi, and A. Bononi, "PDM-iRZ-QPSK vs. PS-QPSK at 100 Gbit/s over dispersion-managed links," Opt. Express **20**, 7895-7900 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-7-7895

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### References

- M. Karlsson, E. Agrell, “Which is the most power-efficient modulation format in optical links?” Opt. Express 17(13), 10814–10819 (2009). [CrossRef] [PubMed]
- E. Agrell, M. Karlsson, “Power-efficient modulation formats in coherent transmission systems,” J. Lightwave Technol. 27(22), 5115–5126 (2009). [CrossRef]
- P. Poggiolini, G. Bosco, A. Carena, V. Curri, F. Forghieri, “Performance evaluation of coherent WDM PS-QPSK (HEXA) accounting for non-linear fiber propagation effects,” Opt. Express 18(11), 11360–11371 (2010). [CrossRef] [PubMed]
- P. Serena, A. Vannucci, A. Bononi, “The performance of polarization switched-QPSK (PS-QPSK) in dispersion managed WDM transmissions,” in Proc. ECOC 2010, Torino, Italy, (2010). Paper Th.10.E.2.
- D. S. Millar, D. Lavery, S. Makovejs, C. Behrens, B. C. Thomsen, P. Bayvel, S. J. Savory, “Generation and long-haul transmission of polarization-switched QPSK at 42.9 Gb/s,” Opt. Express 19(10), 9296–9302 (2011). [CrossRef] [PubMed]
- C. Xie, “Interchannel nonlinearities in coherent polarization-division-multiplexed quadrature-phase-shift- keying systems,” IEEE Photon. Technol. Lett. 21(5), 274–276 (2009). [CrossRef]
- O. Bertran-Pardo, J. Renaudier, G. Charlet, P. Tran, H. Mardoyan, M. Salsi, M. Bertolini, S. Bigo, “Insertion of 100Gb/s coherent PDM-QPSK channels over legacy optical networks relying on low chromatic dispersion fibres,” in Proc. IEEE Globecom, (2009).
- A. Bononi, N. Rossi, P. Serena, “Transmission limitations due to fiber nonlinearity,” in Proc. OFC-NFOEC 2011, Los Angeles, CA, (2011). Paper OWO7.
- P. Serena, M. Bertolini, A. Vannucci, “Optilux toolbox,” (2009). [online] www.optilux.sourceforge.net .
- P. Serena, N. Rossi, O. Bertran-Pardo, J. Renaudier, A. Vannucci, A. Bononi, “Intra- versus Inter-channel PMD in Linearly Compensated Coherent PDM-PSK Nonlinear Transmissions,” J. Lightwave Technol. 29(11), 1691–1700 (2011). [CrossRef]
- P. Johannisson, M. Sjödin, M. Karlsson, H. Wymeersch, E. Agrell, P. A. Andrekson, “Modified constant modulus algorithm for polarization-switched QPSK,” Opt. Express 19(8), 7734–7741 (2011). [CrossRef] [PubMed]
- A. J. Viterbi, A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983). [CrossRef]

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